This scenario describes the transport of two solutes (Synthetica and Syntheticb) through a saturated media. Both solutes react to Productd according to $\text{Product d}=\text{Synthetic a}+0.5~\text{Synthetic b}$. The speed of the reaction is described with a first–order relationship $\frac{dc}{dt}=U(\frac{c_{\text{Synthetic a}}}{K_m+c_{\text{Synthetic b}}})$. The coupling of OGS6 and IPhreeqc used for simulation requires to simulate the transport of $H^+$–ions, additionally. This is required to adjust the compulsory charge balance computation executed by Phreeqc. The solution by OGS6–IPhreeqc will be compared to the solution by a coupling of OGS5–IPhreeqc.
1d scenario: The 1d–model domain is 0.5 m long and discretised into 200 line elements. The domain is saturated at start–up ($p(t=0)=$ 1.0e5 Pa). A constant pressure is defined at the left side boundary ($g_{D,\text{upstream}}^p$) and a Neumann BC for the water mass outflux at the right side ($g_{N,\text{downstream}}^p$). Both solutes, Synthetic a and Synthetic b are present at simulation start–up at concentrations of $c_{\text{Synthetic a}}(t=0)=c_{\text{Synthetic b}}(t=0)= 0.5~\textrm{mol kg}^{1}~\textrm{water}$, the influent concentration is $0.5~\textrm{mol kg}^{1}~\textrm{water}$ as well. Product d is not present at start–up ($c_{\text{Productd}}(t=0)=0$); neither in the influent. The initial concentration of $\text{H}^+$–ions is $1.0e\textrm{}7~\textrm{mol kg}^{1}~\textrm{water}$; the concentration at the influent point is the same. Respective material properties, initial and boundary conditions are listed in the tables below.
2d scenario: The 2d–scenario only differs in the domain geometry and assignment of the boundary conditions. The horizontal domain is 0.5 m in x and 0.5 m in y direction, and, discretised into 10374 quadratic elemtents with an edge size of 0.0025 m.
Parameter  Description  Value  Unit 

$\phi$  Porosity  1.0  
$\kappa$  Permeability  1.157e12  $\textrm{m}^2$ 
$S$  Storage  0.0  
$a_L$  long. Dispersion length  0.0  m 
$a_T$  transv. Dispersion length  0.0  m 
$\rho_w$  Fluid density  1.0e+3  $\textrm{kg m}^{3}$ 
$\mu_w$  Fluid viscosity  1.0e3  Pa s 
$D_{\text{H}^+}$  Diffusion coef. for $\text{H}^+$  1.0e7  m$^2$ s 
$D_{solutes}$  Diffusion coef. for Synthetica, Syntheticb and Productd  1.0e12  m$^2$ s 
$U$  Reaction speed constant  1.0e3  h$^{1}$ 
$K_m$  Half–saturation constant  10  mol kg$^{1}$ water 
Table: Media, material and component properties
Parameter  Description  Value  Unit 

$p(t=0)$  Initial pressure  1.0e+5  Pa 
$g_{N,downstream}^p$  Water outflow mass flux  1.685e02  mol kg$^{1}$ water 
$g_{D,upstream}^p$  Pressure at inlet  1.0e+5  Pa 
$c_{Synthetica}(t=0)$  Initial concentration of Synthetica  0.5  mol kg$^{1}$ water 
$c_{Syntheticb}(t=0)$  Initial concentration of Syntheticb  0.5  mol kg$^{1}$ water 
$c_{Productd}(t=0)$  Initial concentration of Productd  0  mol kg${^1}$ water 
$c_{\text{H}^+}(t=0)$  Initial concentration of $\text{H}^+$  1.0e7  mol kg$^{1}$ water 
$g_{D,upstream}^{Synthetica_c}$  Concentration of Synthetica  0.5  mol kg$^{1}$ water 
$g_{D,upstream}^{Syntheticb_c}$  Concentration of Syntheticb  0.5  mol kg$^{1}$ water 
$g_{D,upstream}^{Productd}$  Concentration of Productd  0.0  mol kg$^{1}$ water 
$g_{D,upstream}^{\text{H}^+}$  Concentration of $\text{H}^+$  1.0e7  mol kg$^{1}$ water 
Table: Initial and boundary conditions
The kinetic reaction results in the expected decline of the concentration of Synthetic a and Synthetic b, which is superpositioned by the influx of these two educts through the left side. By contrast, the concentration of Product d increases in the domain. Over time, opposed concentration fronts for educts and Product d evolve. Both, OGS6 and OGS5 simulations yield the same results in the 1d as well as 2d scenario. For instance, the difference between the OGS6 and the OGS5 computation for the concentration of Product d expressed as root mean squared error is 1.76e7 mol kg$^{1}$ water (over all time steps and mesh nodes, 1d scenario); the corresponding median absolute error is 1.0e7 mol kg$^{1}$ water. This verifies the implementation of OGS6–IPhreeqc.
This article was written by Johannes Boog. If you are missing something or you find an error please let us know.
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Last revision: July 12, 2023
Commit: [PL/SSD] Rename x_dot to x_prev 04a8fec8
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